No Gnome is a desktop environment which is similar to the Mac desktop environment. Ditto KDE and windows.

This distinction is confusing for new Linux users because windows and Mac each only provide one desktop environment so users conflate the desktop and OS. Imagine if you could change your computer from having a windows desktop to a Mac desktop while having all your files and applications stay exactly the same and still work. This is how Linux works. Whether you use Gnome (a Mac like interface) or KDE (a windows like interface) or one of the tiling/scrolling compositors of Linux power users it’s just the UI layer of the OS, it’s a totally independent question from what distro/software you’re running and you can freely mix and match

Very much no. Your distro provides your package manager and repositories. Many distros ship with a default desktop environment, many let you choose on install. Either way the user can always manually switch very easily

This is a question about desktop environments not distros. Many distros ship a default desktop environment but you can always change it. Among the desktop environments it’s typically said:

Gnome ~ Mac, KDE ~ Windows

As for a Linux flavored one I think the most distinctly linux desktops are the tiling and scrolling compositors (hyprland, niri etc)